Consider a basic classification of ghosts and tachyons
following [1]}, [2]}.
The general action of a free second-order field
\(\,h(x)=h(t,{{\bf r}})\,\)  can be written as
\(S(h) &=&\frac{s_1}{2} \int d^4x \,\big \lbrace  \eta ^{\mu \nu }\partial _\mu h \partial _\nu h- s_2 m^2 h^2 \big \rbrace \nonumber \\&&\quad = \,\,\frac{s_1}{2} \int d^4x \,\big \lbrace  {\dot{h}}^2 - (\nabla h)^2- s_2 m^2 h^2 \big \rbrace \,.\) 
